stat/distuv: add binomial distribution

stat/distuv/binomial_test.go

@@ -0,0 +1,134 @@
+// Copyright ©2018 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package distuv
+
+import (
+	"sort"
+	"testing"
+
+	"golang.org/x/exp/rand"
+
+	"gonum.org/v1/gonum/floats"
+)
+
+func TestBinomialProb(t *testing.T) {
+	const tol = 1e-10
+	for i, tt := range []struct {
+		k    float64
+		n    float64
+		p    float64
+		want float64
+	}{
+		// Probabilities computed with Wolfram|Alpha (http://wwww.wolframalpha.com)
+		{0, 10, 0.5, 0.0009765625},
+		{1, 10, 0.5, 0.009765625},
+		{2, 10, 0.5, 0.0439453125},
+		{3, 10, 0.5, 0.1171875},
+		{4, 10, 0.5, 0.205078125},
+		{5, 10, 0.75, 5.839920043945313e-02},
+		{6, 10, 0.75, 0.1459980010986328},
+		{7, 10, 0.75, 0.2502822875976563},
+		{8, 10, 0.75, 0.2815675735473633},
+		{9, 10, 0.75, 0.1877117156982422},
+		{10, 10, 0.75, 5.6313514709472656e-02},
+
+		{0, 25, 0.25, 7.525434581650003e-04},
+		{2, 25, 0.25, 2.508478193883334e-02},
+		{5, 25, 0.25, 0.1645375881987921},
+		{7, 25, 0.25, 0.1654081574485211},
+		{10, 25, 0.25, 4.165835076481272e-02},
+		{12, 25, 0.01, 4.563372575901533e-18},
+		{15, 25, 0.01, 2.956207951505780e-24},
+		{17, 25, 0.01, 9.980175928758777e-29},
+		{20, 25, 0.99, 4.345539559454088e-06},
+		{22, 25, 0.99, 1.843750355939806e-03},
+		{25, 25, 0.99, 0.7778213593991468},
+
+		{0.5, 25, 0.5, 0},
+		{1.5, 25, 0.5, 0},
+		{2.5, 25, 0.5, 0},
+		{3.5, 25, 0.5, 0},
+		{4.5, 25, 0.5, 0},
+		{5.5, 25, 0.5, 0},
+		{6.5, 25, 0.5, 0},
+		{7.5, 25, 0.5, 0},
+		{8.5, 25, 0.5, 0},
+		{9.5, 25, 0.5, 0},
+	} {
+		b := Binomial{N: tt.n, P: tt.p}
+		got := b.Prob(tt.k)
+		if !floats.EqualWithinRel(got, tt.want, tol) {
+			t.Errorf("test-%d: got=%e. want=%e\n", i, got, tt.want)
+		}
+	}
+}
+
+func TestBinomialCDF(t *testing.T) {
+	const tol = 1e-10
+	for i, tt := range []struct {
+		k    float64
+		n    float64
+		p    float64
+		want float64
+	}{
+		// Cumulative probabilities computed with SciPy
+		{0, 10, 0.5, 9.765625e-04},
+		{1, 10, 0.5, 1.0742187499999998e-02},
+		{2, 10, 0.5, 5.468749999999999e-02},
+		{3, 10, 0.5, 1.7187499999999994e-01},
+		{4, 10, 0.5, 3.769531249999999e-01},
+		{5, 10, 0.25, 9.802722930908203e-01},
+		{6, 10, 0.25, 9.964942932128906e-01},
+		{7, 10, 0.25, 9.995841979980469e-01},
+		{8, 10, 0.25, 9.999704360961914e-01},
+		{9, 10, 0.25, 9.999990463256836e-01},
+		{10, 10, 0.25, 1.0},
+
+		{0, 25, 0.75, 8.881784197001252e-16},
+		{2.5, 25, 0.75, 2.4655832930875472e-12},
+		{5, 25, 0.75, 1.243460090449844e-08},
+		{7.5, 25, 0.75, 1.060837565347583e-06},
+		{10, 25, 0.75, 2.1451240486669576e-04},
+		{12.5, 25, 0.01, 9.999999999999999e-01},
+		{15, 25, 0.01, 9.999999999999999e-01},
+		{17.5, 25, 0.01, 9.999999999999999e-01},
+		{20, 25, 0.99, 4.495958469027147e-06},
+		{22.5, 25, 0.99, 1.9506768897388268e-03},
+		{25, 25, 0.99, 1.0},
+	} {
+		b := Binomial{N: tt.n, P: tt.p}
+		got := b.CDF(tt.k)
+		if !floats.EqualWithinRel(got, tt.want, tol) {
+			t.Errorf("test-%d: got=%e. want=%e\n", i, got, tt.want)
+		}
+	}
+}
+
+func TestBinomial(t *testing.T) {
+	src := rand.New(rand.NewSource(1))
+	for i, b := range []Binomial{
+		{100, 0.5, src},
+		{15, 0.25, src},
+		{10, 0.75, src},
+		{9000, 0.102, src},
+		{1e6, 0.001, src},
+		{25, 0.02, src},
+		{3, 0.8, src},
+	} {
+		testBinomial(t, b, i)
+	}
+}
+
+func testBinomial(t *testing.T, b Binomial, i int) {
+	const tol = 1e-2
+	const n = 1e6
+	x := make([]float64, n)
+	generateSamples(x, b)
+	sort.Float64s(x)
+
+	checkMean(t, i, x, b, tol)
+	checkVarAndStd(t, i, x, b, tol)
+	checkExKurtosis(t, i, x, b, 7e-2)
+}